This article is cited in 23 papers

Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains

A. Mielke^a, S. V. Zelik<sup>b

a</sup> University of Stuttgart, Mathematical Institute A
^b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: This paper is a study of an abstract model of a second-order non-linear elliptic boundary-value problem in a cylindrical domain by the methods of the theory of dynamical systems. It is shown that, under some natural conditions, the essential solutions of the problem in question are described by means of the global attractor of the corresponding trajectory dynamical system, and this attractor can have infinite fractal dimension and infinite topological entropy. Moreover, sharp upper and lower bounds are obtained for the Kolmogorov $\varepsilon$-entropy of these attractors.

MSC: Primary 35J25, 35J65; Secondary 35B41, 37A35, 37B40, 37C45, 35K57

Received: 05.04.2002

DOI: 10.4213/rm550

 English version: Russian Mathematical Surveys, 2002, 57:4, 753–784

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